Optimizers

1. Momentum:

- Definition: Momentum is an extension of the gradient descent optimization algorithm. It builds inertia in the search direction to overcome local minima and noisy gradient oscillations. It's inspired by the concept of momentum in physics, where a rolling ball accumulates momentum to overcome obstacles.

- Application:

- Useful for complex loss landscapes with multiple local minima.

- Accelerates optimization by considering exponentially weighted gradients from the past.

- Addresses issues like noise and non-convex functions.

- Scenario: Imagine training a deep neural network with many parameters. Momentum helps navigate the loss surface efficiently, avoiding getting stuck in local minima.

2. Adagrad (Adaptive Gradient):

- Definition: Adagrad adapts the learning rate for each parameter based on the historical gradients. It performs smaller updates for frequently occurring features and larger updates for infrequently occurring ones.

- Application:

- Well-suited for large-scale problems with many parameters.

- Automatically tunes the learning rate, reducing the need for manual adjustments.

- Effective in non-convex optimization and neural network training.

- Scenario: Consider training a language model with a vast vocabulary. Adagrad adjusts learning rates for individual word embeddings, ensuring efficient convergence.

3. NAG (Nesterov Accelerated Gradient):

- Definition: NAG is an extension of standard gradient descent. It incorporates momentum by considering the gradient ahead of the current position during updates.

- Application:

- Improves convergence speed by anticipating the next gradient direction.

- Helps escape saddle points and accelerates optimization.

- Widely used in deep learning and neural network training.

- Scenario: Imagine training an image classification model. NAG helps navigate the loss landscape more efficiently, leading to faster convergence.

4. RMSProp (Root Mean Square Propagation):

- Definition: RMSProp adapts the learning rate by considering an exponential moving average of squared gradients. It improves upon Adagrad by avoiding the accumulation of squared gradients.

- Application:

- Effective for non-stationary data and complex loss surfaces.

- Prevents the learning rate from shrinking too aggressively.

- Widely used in neural network training.

- Scenario: Suppose you're training a recurrent neural network for time series prediction. RMSProp helps balance learning rates across different features, preventing overshooting and ensuring stable convergence.

5. Adam (Adaptive Moment Estimation):

- Definition: Adam combines momentum and RMSProp. It adapts the learning rate for each parameter individually, providing an efficient gradient descent method.

- Application:

- Widely used in deep learning due to its robustness and efficiency.

- Balances step size for global and local minima exploration.

- Suitable for various tasks, including image recognition and natural language processing.

- Scenario: Consider training a generative adversarial network (GAN). Adam optimizes both the generator and discriminator, allowing efficient convergence and stable training.

6. Batch Gradient Descent (BGD):

- Definition: BGD computes the gradient of the cost function using the entire training dataset in each iteration. It updates model parameters by considering the average gradient over all examples.

- Application:

- Suitable for small to medium-sized datasets.

- Converges to a global minimum if the loss surface is convex.

- Commonly used in linear regression and simple neural networks.

- Scenario: When training a linear regression model on a moderate-sized dataset, BGD provides stable convergence.

7. Stochastic Gradient Descent (SGD):

- Definition: SGD computes the gradient using only a single random training example (or a small batch) in each iteration. It introduces randomness into the optimization process.

- Application:

- Efficient for large datasets due to reduced computational cost per iteration.

- Escapes local minima and saddle points.

- Commonly used in deep learning and neural network training.

- Scenario: Imagine training a deep convolutional neural network for image classification. SGD efficiently navigates the loss landscape, avoiding getting stuck in local optima.

8. Mini-Batch Gradient Descent (MB-GD):

- Definition: MB-GD splits the training dataset into small batches. It computes the gradient using a mini-batch (subset) of examples in each iteration.

- Application:

- Balances computational efficiency and stability.

- Works well for medium to large datasets.

- Widely used in deep learning and neural networks.

- Scenario: Suppose you're training a recurrent neural network for natural language processing. MB-GD strikes a balance between efficiency and accurate updates.